Reported crowd trouble in the build-up to the showpiece occasion meant that kickoff was delayed for around 40 minutes, but once underway it proved to be worth the wait.
Napoli did find a way through shortly after, however, and it was Insigne who found the back of the net when he opened up his body and curled a fine effort past the Brazilian keeper.
The second goal came six minutes later when Higuain showed the skill and strength needed to break free down the right, before pulling the ball back for Insigne to double his tally.
The Viola very nearly levelled things up on 72 minutes when Matias Fernandez powered in a strike from long range, but Reina was alert to tip the ball over the bar.
The save almost proved vital with Goran Pandev being played through on goal soon after, only to see his strike kept out by Neto to keep the final alive heading into the final 15 minutes.
Then came another big moment when Gokhan Inler was shown a second yellow card following a foul from behind on Ilicic, paving the way for a late Fiorentina surge.
Illic had a brilliant opportunity to take the game into extra time when he was picked out by Alessandro Matri in acres of space, though his bending effort was wide of the target.
The Partenopei could begin celebrating two minutes from time when Dries Mertens grabbed a third goal after firing the ball past Neto, ensuring Napoli would return to Naples with the trophy.